Total number of covalent bonds in `C_(3)O_(2)` is x and y is the number of sp - hybridised atom. Find the sum of `x+y`?

Answer

To solve the problem, we need to determine the total number of covalent bonds in the molecule \( C_3O_2 \) (carbon suboxide) and the number of sp-hybridized atoms. We will then find the sum of these two values.

### Step 1: Identify the structure of \( C_3O_2 \)

The molecular structure of carbon suboxide (\( C_3O_2 \)) can be represented as follows:
\[ O=C=C=C=O \]
This structure consists of three carbon atoms and two oxygen atoms.

### Step 2: Count the covalent bonds

Covalent bonds can be classified into sigma (σ) and pi (π) bonds.

- Each double bond consists of one sigma bond and one pi bond.
- In the structure of \( C_3O_2 \):
- There are two double bonds between the carbon and oxygen atoms (C=O) and one double bond between the carbon atoms (C=C).

Counting the bonds:
- **C=O bonds**: 2 double bonds contribute:
- 2 sigma bonds
- 2 pi bonds
- **C=C bond**: 1 double bond contributes:
- 1 sigma bond
- 1 pi bond

Now, let's tally the total:
- **Sigma bonds**:
- From C=O: 2
- From C=C: 1
- Total sigma bonds = 2 + 1 = 3

- **Pi bonds**:
- From C=O: 2
- From C=C: 1
- Total pi bonds = 2 + 1 = 3

Thus, the total number of covalent bonds \( x \) is:
\[ x = \text{Total Sigma Bonds} + \text{Total Pi Bonds} = 3 + 3 = 6 \]

### Step 3: Determine the number of sp-hybridized atoms

In the structure of \( C_3O_2 \):
- Each carbon atom is involved in a double bond, which means they are sp-hybridized.
- There are 3 carbon atoms in total, and since all are sp-hybridized, we have:
\[ y = 3 \]

### Step 4: Calculate the sum \( x + y \)

Now we can find the sum of \( x \) and \( y \):
\[ x + y = 6 + 3 = 9 \]

### Final Answer

The sum of \( x + y \) is \( 9 \).

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